To further improve the pose estimation of our inverse rendering pipeline,
we follow state-of-the-art SLAM systems [1]}, [2]}, [3]} that optimize the rigid transformation \((R,t) \in SE(3)\)  in tangent-space.
Linearized pose increments are expressed as the Lie-algebra elements \(x \in \mathfrak {se}(3)\)  and applied to a transformation by
\((R^{\prime },t^{\prime })= \exp (x) \cdot (R,t),\) 
